In this work, an extension of the Cartesian sensitivity encoding (SENSE) parallel imaging framework is proposed. In the well-known SENSE solution, the overdetermined reconstruction inversion problem is optimized to get the highest signal-to-noise ratio in the image. In this extension, the probability of artifacts due to incorrect knowledge of the receiver coil sensitivities is also taken into account. This is realized by assuming an uncertainty in measured receiver coil sensitivities to enable weighting of residual artifact level and signal-to-noise ratio in the inversion problem. This inversion problem can still be solved by a least-squares optimization without the need of any complex iterative scheme. Results in abdominal imaging show that artifact levels can be substantially reduced, at the cost of a signal-to-noise ratio penalty. The size of the signal-to-noise ratio penalty depends on the assumed inaccuracy of the coil sensitivities, sensitivity encoding acceleration factor, and coil configuration. Magn Reson Med, 2013. © 2012 Wiley Periodicals, Inc.